To answer my own question, in case anyone else finds that their remote keyfob no longer works: I bought a used/refurbished remote on eBay (Part #41804) for £15, then reprogrammed it using the instructions below. The new remote works great, and at a cost £200 lower than I was quoted by my local Mazda dealer (£216).
Step 1: Open driver side door and leave open.
Step 2: Lock and Unlock the drivers door using the power door lock switch on the door
Step 3: Insert key into the ignition.
Step 4: Turn Key to ON position and return to Lock (off) position. Do this 3 times within 10 seconds. LEAVE key in the ignition in Lock (off) position.
Step 5: Close and open the drivers door 3 times. Leave door open after this step
Step 6: ECU should respond by locking and unlocking the doors once.
Step 7: Press any button on remote #1 twice. ECU responds by locking and unlocking the car doors.
Step 8: Additional remotes, repeat Step 7 for up to 3 remotes total.
Step 9: Remove the key from the ignition and the ECU will respond a final time with a series (about 4) of door locks and unlocks. You're done